I may be wrong, but I think living with this top group is the best black can do... I see no way for the bottom group to live. I'd be interested in seeing if there's any better outcome :) --Hikaru79
LukeNine45: Exactly what I had in mind.
This also seems to be a option, with the same choices for white (ko for the whole thing, or let the top live unconditionally):
ChrisSchack: (In response to the original diagram): White wouldn't play this way if not planning to start the ko, it gives up 4 points for the same result.
LukeNine45: You're right, this is a much more consistent way for white to play. (If you delete our exchange after you read it, the page will make a little more sense for the passer-by :)
Bill: The first diagrams are the normal way of playing. Typically White will not be able to fight the ko effectively, and Black will live without the ko.
If White can afford to play the ko, Black should still start with the atari in the first diagram. White's response is as in the second diagram.
If, instead, White plays , - is Black's ko threat.
This shows that is not a good first play for Black. First, it loses the chance for this ko threat. Second, if White loses the ko, it gives up a sure 1/2 point to White at a, which White does not get if her first play is . This makes the ko worth slightly less and slightly more favorable for White. And, of course, if White avoids the ko, makes more territory. Either way, is better for Black than .
All of these are very minor points, but fairly clear. Avoiding should be a no-brainer.